Sample vs. population, Now | HP 49g guide

The form lists the data in Σ DAT, shows that column 1 is selected (there is only one column in the current Σ DAT). Move about the form with the arrow keys,

and press the	soft menu key to select those measures (Mean, Standard
measures:	@CHK@
Deviation, Variance, Total number of data points, Maximum and Minimum
values) that you want as output of this program. When ready, press		.

The selected values will be listed, appropriately labeled, in the screen of your calculator. For example:

Sample vs. population

The pre-programmed functions for single-variable statistics used above can be applied to a finite population by selecting the Type: Population in the SINGLE-VARIABLE STATISTICS screen. The main difference is in the values of the variance and standard deviation which are calculated using n in the

denominator of the variance, rather than (n-1). For the example above, use
now the		soft menu key to select population as Type: and re-calculate@@@OK@@
	@CHOOSE
	@CHOOSE				Page 16-2

Image 159

HP 49g manual Sample vs. population, Now

Contents

Graphing calculator User’s manualPage Preface Page Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Vector Analysis Applications GraphicsCalculus Applications Multi-variate Calculus Applications Differential Equations Probability DistributionsStatistical Applications Limited Warranty W-1 Service, W-2 Regulatory information, W-4Numbers in Different Bases Chapter Getting started Basic OperationsBatteries Contents of the calculator’s display Menus Tool menuAssociated with the six soft menu keys, F1 through F6 Introducing the calculator’s keyboard Setting time and datePage Selecting calculator modes Alpha function, to enter the upper-case letter P~„p 23.0 Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Selecting Display modes Explanation of CAS settings Selecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW References Creating arithmetic expressions Chapter Introducing the calculatorCalculator objects Editing expressions in the stack Result³5*„Ü1+1/7will be shown„ÜR3as follows -2Q3`.5 Resulting…in³5*„Ü1+1/7the output„ÜR3-2Q3`.5 + y Creating algebraic expressions Using the Equation Writer EQW to create expressions Edited expression*„Ü5+1/3looks as follows + 2 ⋅ 5 + ~‚n For this example, the Home Organizing data in the calculatorHome directory Subdirectories Locks the alphabetic keyboard in lower case. When locked VariablesTyping variable names Creating variables Name Contents Type 3V5K~a12` ³~„r/„Ü ‚å‚é~„r³„ì Checking variables contents Using the right-shift key followed by soft menu key labels @PURGE@J@@p1@@` Using function Purge in the stack in Algebraic modeUsing function Purge in the stack in RPN mode Deleting variables Undo and CMD functions Choose boxes vs. Soft MenuWe use Show Prog menu list and select Memory ‚¯ Page Not shown in this screen. To Find it we use Display now shows To activate the Order command we press the soft menu key Operation key, namely Examples in ALG mode Chapter Calculations with real numbersExamples of real number calculations Directly on the stack For both, ALG and RPN modes, using the Equation Writer Combination When calculating in the stack in ALG mode Key. WhenRPN mode, enter the number first, then the function, e.g „¸Page \„¸45`‚¹ RPN mode Hyperbolic functions and their inverses Real number functions in the MTH menu Pressing shows the remaining options With units Units menuKey or Page Key or Keystroke sequence to navigate Through the menus Available unitsFor Set of units Labels will be listed With the keyboard, e.g.,will produce the entry Attaching units to numbers Operations with units Using Ubase to convert to the default unit 1 m results 12m 3250mi Different terms in parentheses, e.g These operations produce the following output @@OK@@-˜Physical constants in the calculator Unit conversions Exit constants library When selected, constants are shown with units attachedWhen selected, constants are shown without units Copies value with or without units to the stack Defining and using functions Like this Display shows what is called a tagged value HereWhich produces ‘LNx+1 + EXPx’ ‚@@@H@@ You could try Entered by using Definitions Setting the calculator to Complex modeTo work with complex numbers select the CAS complex mode Chapter Calculations with complex numbers Entering complex numbers Polar representation of a complex numberTo enter the unit imaginary number type the I key Simple operations with complex numbers Cmplx menu through the MTH menu Cmplx menus Cmplx menu in the keyboard Function Droite equation of a straight line Functions applied to complex numbers Reference Function Droite is found in the command catalog Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects Variable menu Press To recover Functions in the ALG menu @HELP@` Catalog To complete the operation To execute the command Operations with transcendental functions Expansion and factoring using log-exp functionsExpansion and factoring using trigonometric functions Trig menu, triggered by using Functions in the Arithmetic menu Shows the following menuNumbers or to polynomials. The remaining options 1. Integer Polynomials Horner functionX6-1 = X5-5*X4+25X3-125X2+625X-3125X+5+15624 Quotient and Remainder functions VariablePcoef function Proot function Fractions Peval functionSIMP2 function Propfrac function Partfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions Reference Chapter Solution to equations Symbolic solution of algebraic equationsFunction Isol Function Solve Page Function Zeros Function Solvevx Numerical solver menu Polynomial Equations Enter vector of coefficientsSolve equation Page Page Solving equations with one unknown through NUM.SLV Financial calculations Solution shown is X 4.5006E-2 Solution to simultaneous equations with MslvPage Reference Chapter Operations with lists Creating and storing listsChanging sign Addition, subtraction, multiplication, division When applied to lists, acts a concatenation operator Functions‚Napplied to listsExample Inverse 1/x Lists of complex numbersLists of algebraic objects MTH/LIST menu Sorts elements in increasing order Calculate increment among consecutive elements in listCalculate summation of elements in the list Calculate product of elements in the list SEQ function, available through the command catalog , takes SEQ functionMAP function Reference General row vector Vector Vector of algebraics Chapter VectorsEntering vectors Typing vectors in the stack Stored into variables Mode Then, ‚íinVectors can also be entered by using the matrix writer Storing vectors into variables in the stack WID Key is used to edit the contents of a selected cell Selected Key will add a column full of zeros at the locationCell of the spreadsheet Function Delete Will delete Simple operations with vectors Addition, subtractionUsed in the following exercises Absolute value function Multiplication by a scalar, and division by a scalar Examples MTH/VECTOR menuMagnitude Dot product Cross product Entering matrices in the stack Chapter Matrices and linear algebra Typing in the matrix directly into the stack Display in RPN mode will look very similar to these Addition and subtraction Operations with matrices RPN mode, try the following eight examples Multiplication Cij = aik ⋅ bkj , for i = 1,2, , m j = 1,2, , n Page Function Trace Solution of linear systemsCharacterizing a matrix The matrix Norm menu Function DET Can be written as the matrix equation A⋅x = b, if Using the numerical solver for linear systemsPress Following input form will be provide right 2x1 + 3x2 -5x3= @SOLVE Solution by division of matrices Solution with the inverse matrix Graphs options in the calculator Chapter Graphics Them simultaneously if in RPN mode Use a range of -4 to Plotting an expression of the form y = fxAs an example, lets plot the function Press Then To recover the menu, and return to the PlotAlso, check that for x = -1.48 , y = Here is picture Suggested early, namely x = You will be returned to normal calculator displayZoom factor = 0.5. Toggle To see the table, press Soft menu key To return to normal calculator display press Fast 3D plotsKey simply changes the font in the table from small to big, Option Decimal Produces x-increments Option Integer Find Fast3D Values of 10 and 8 for the Step dataYou can change Orientation @EDITL Press To leave the Edit environment Reference$ Function lim Chapter Calculus ApplicationsCalc Calculus menu Limits and derivatives Infinity symbol is associated with Key, .e Including some limitsMenu within the Calcl menu Anti-derivatives and integrals Functions INT, INTVX, RISCH, Sigma and SigmavxIf and only if, fx = dF/dx, and C = constant Xdx = F b − F a ⋅ x − x o n Functions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Y dA = b Φ x , y dydx = Multiple integrals Chapter Vector Analysis Applications Del operatorGradient Divergence CurlAlternatively, use function Deriv as follows Solution to linear and non-linear equations Chapter Differential EquationsCALC/DIFF menu Function Ldec Ldec Function Desolve Which can be simplified to= K1⋅e-3x+ K2⋅e5x + K3⋅e2x + 450⋅x2+330⋅x+241/13500 DESOLVE` Variable Odetype Laplace transform and inverses in the calculator Laplace Transforms Function FOURIER` Fourier series for a quadratic functionWhere Exercises. Function Collect is available in the ALG menu Thus = 1/3, c Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations Random numbers MTH/PROB menu part „´The Normal distributionStudent-t distribution F distribution Chi-square distribution Entering data‚Ù5 Chapter Statistical Applications Now Sample vs. population Obtaining frequency distributions Fitting data to a function y = fx Ƒ3.FitdataCan be used Lines in RPN mode Obtaining additional summary statistics When that field is selected StatisticsTo access the summary stats… option, use Using Key select all the options for outputs, i.e Confidence intervals Press to obtain the following resultsOffers the following options Interpreted as follows Interval information @GRAPH Return to the previous results screen, and/or press Corresponding interval limits 21.88424 and 24.51576. Press @@@OK@@@ Select ∝ ≠ 150. Then, press Result is With system flag 117 set to Soft menus, the Base menu shows Chapter Numbers in Different BasesBase menu Writing non-decimal numbers @HEX Using SD cards ChapterStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD card Limited Warranty Service Rotc = Rest of the country Canada 905 206-4663 or 800- HP USA Regulatory information